The plan is for this to be an introductory textbook on elementary number theory
from a geometric point of view, as opposed to the usual strictly algebraic approach.
The title "Topology of Numbers" is intended to convey this idea of a more geometric slant, where we are using the word "Topology" in the general sense of "geometrical arrangement" rather than its usual mathematical meaning of a set with certain specified subsets called open sets. A fair portion of the book is devoted to studying Conway's topographs associated to quadratic forms in two variables, so perhaps the title could have been "Topography of Numbers" instead.

The current version of the book is still just a preliminary draft, so it is
incomplete and lacking in polish at many points.

You can download a pdf file of what currently exists of the book, about 175 pages. This version was posted in February 2018. The main changes from the previous versions occur in Chapters 5 and 6 which have been considerably expanded.